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arXiv · 1803.09086

The inf-sup condition and error estimates of the Nitsche method for evolutionary diffusion-advection-reaction equations

Yuki Ueda·Norikazu Saito
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Abstract

The Nitsche method is a method of "weak imposition" of the inhomogeneous Dirichlet boundary conditions for partial differential equations. This paper explains stability and convergence study of the Nitsche method applied to evolutionary diffusion-advection-reaction equations. We mainly discuss a general space semidiscrete scheme including not only the standard finite element method but also Isogeometric Analysis. Our method of analysis is a variational one that is a popular method for studying elliptic problems. The variational method enables us to obtain the best approximation property directly. Actually, results show that the scheme satisfies the inf-sup condition and Galerkin orthogonality. Consequently, the optimal order error estimates in some appropriate norms are proven under some regularity assumptions on the exact solution. We also consider a fully discretized scheme using the backward Euler method. Numerical example demonstrate the validity of those theoretical results.

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Yuki Ueda, Norikazu Saito. 2018-03-24. The inf-sup condition and error estimates of the Nitsche method for evolutionary diffusion-advection-reaction equations. https://arxiv.org/abs/1803.09086

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